Reduction of peak to average power ratio

ABSTRACT

A method for Peak to Average Power Ratio (PAPR) reduction at an input of analog to digital converter (ADC) of the receiver, the method includes mapping, by a mapper, an input symbol to an output symbol that maintains a peak power constraint at the input of the ADC; wherein the mapping is responsive to (a) previously transmitted symbols and (b) a state of the channel following a transmission of the current output symbol; transmitting the output symbol by the transmitter; receiving, by the receiver, a received symbol that represents the output symbol; and de-mapping the received symbol, by a de-mapper of the receiver, to a de-mapped symbol that represents the input symbol.

CROSS-REFERENCE

This application is a continuation in part of U.S. patent applicationSer. No. 16/706,838 filing date Dec. 9, 2019 to be granted on Mar. 9,2021, which claims priority from U.S. provisional Ser. No. 62/777,174filing date Dec. 9, 2018—both are incorporated herein by reference.

BACKGROUND

Wireline communication channels such as, chip-to-chip SerDescommunication channels, optical communication channels, and magneticrecording channels, can be modeled by additive white gaussian noise(AWGN) channels with intersymbol interference (ISI)

Recently, advanced very high speed links are starting to employ ADCs atthe receiver to convert the analog signal to a digital signal. Animportant parameter of an ADC device is the Signal to Noise andDistortion Ratio (SNDR) or equivalently effective number of bits (ENOB).

To avoid excessive signal distortion due to clipping, the ADC isrequired to have a large dynamic range to achieve the desired systemperformance. The demand of a large dynamic range translates to highercircuit design complexity and higher power consumption.

Signals at the ADC input are therefore backed-off (BO) with respect tothe ADC saturation point.

For an ADC with a given input signal range and ENOB, the input signalpower BO improves the signal to clipping distortion ratio but degradesthe receiver signal to quantization noise ratio (RSQNR), as well assignal to thermal noise ratio of the ADC output, as the noise power dueto quantization noise and thermal noise are independent in the inputsignal power. Thus, decreasing the signal to clipping distortion whilekeeping on both signal to quantization noise and signal to thermal noiseratios is a desired approach, which can be performed by decreasing thePAPR of the signal at the ADC input.

The ever increasing demand for higher data rates in wirelinecommunication channels is not going to stop in the foreseen future. Rawdata rates of 100 Gbps, 200 Gbps and 400 Gbps are intended to be used inthe next Ethernet generation.

However, the PAPR is increased especially as the symbol rate gets higheron the same physical channel. For example, a comparison between the PAPRdistributions at the ADC input, in different transmission rates, isshown in FIG. 1.

In this example, the transmission is over a SerDes channel (typical 50cm chip to chip trace), and the transmitted symbols are chosen uniformlyfrom 8-PAM constellation. It can be seen that the PAPR in these cases,depending on the transmission rate, may reach well over 10 dB.

The mainly reason of high PAPR is due to ISI at the receiver, whichcauses by the channel impulse response. Thus, several approaches foreliminating the ISI can be used for PAPR reduction at the receiver. Oneapproach is Zero-Forcing (ZF) equalizer, which is a filter with spectralresponse inverse of the channel response, can be used on the analogsignal, prior the ADC, in order to completely remove ISI and reduce thePAPR. However, the circuit design complexity of such an analog equalizeris high. Moreover, the equalizer generates high noise enhancement infrequencies where the channel response has high attenuation.

A possible solution to overcome the noise enhancement is by using the ZFfilter in the transmitter. However, in this case the PAPR at thetransmitter will be high. To avoid saturation of the transmitted signalby the power amplifier, the transmitted signal at the power amplifierinput is backed-off (BO), so that instantaneous high peak values willnot result in saturation. The cost of the BO is that the average powerof the signal is lower, thus compromising the error performance.

Another equalizer that can be used for ISI (or PAPR) reduction at theADC input is a continues time linear equalizer (CTLE). The CTLE is ananalog high pass filter, approximating the ZF, constructed from analogcomponents, both passive (resistors, capacitors, inductors) and active(amplifier), used prior to ADC, that boost up high-frequencies tocounter the channel attenuation and distortion.

Consequently, the impulse response of the equivalent channel, resultingfrom concatenating the channel and the CTLE filter impulse responses,spans over much lower symbol periods compared to the channel impulseresponse. Hence, both ISI and PAPR are lower at the ADC input.

There are two main disadvantages with passive CTLE. First, the RCnetwork introduces large impedance discontinuity at the channel andequalizer interface. Impedance matching networks, often employinginductors, can be used to prevent the discontinuity. However, the largeinductors make this approach less suitable for on-chip integration.Second, this method cannot improve SNR, since equalization is performedby attenuating low-frequency signal spectrum.

It is desirable therefore to have a gain greater than one at allfrequencies to maximize the benefit from receiver-side equalization.Hence, CTLE using active circuit elements rather than passive componentsare required. However, active CTLE amplifies the high frequency noisewhich potentially degrading the noise margin.

There is a growing need to provide an efficient system, method and acomputer readable medium for maintaining a desired PAPR constrains aninput of an ADC of a receiver.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments of the disclosure will be understood and appreciatedmore fully from the following detailed description, taken in conjunctionwith the drawings in which:

FIG. 1 is an example of a method;

FIG. 2 is an example of a turbo encoder;

FIG. 3 is an example of a receiver;

FIG. 4 is an example of a method;

FIG. 5 is an example of a precoder;

FIG. 6 is an example of a system;

FIG. 7 is an example of a part of the precoder; and

FIG. 8 is an example of a method.

DETAILED DESCRIPTION OF THE DRAWINGS

Any reference to a device should be applied, mutatis mutandis to amethod that is executed by a device.

Any reference to method should be applied, mutatis mutandis to a devicethat is configured to execute the method.

The term “and/or” is additionally or alternatively.

The terms “including”, “comprising”, “having”, “consisting” and“consisting essentially of” are used in an interchangeable manner. Forexample—any method may include at least the steps included in thefigures and/or in the specification, only the steps included in thefigures and/or the specification. The same applies to the device.

It will be appreciated that for simplicity and clarity of illustration,elements shown in the figures have not necessarily been drawn to scale.For example, the dimensions of some of the elements may be exaggeratedrelative to other elements for clarity. Further, where consideredappropriate, reference numerals may be repeated among the figures toindicate corresponding or analogous elements.

There may be provided a method for Peak to Average Power Ratio (PAPR)reduction at an input of analog to digital converter (ADC) of thereceiver.

FIG. 1 is an example of method 100.

Method 100 may start by step 110 of mapping, by a mapper, an inputsymbol to an output symbol that maintains a peak power constraint at theinput of the ADC of the receiver.

The mapping may be responsive to previously transmitted symbols.

The mapping may be set regardless of a maximization of entropy.

The mapping may be responsive to a channel impulse response and to amaximal power allowed by the input of the ADC. The ADC is a part of thereceiver that converts analog signals from a channel to digital signalsthat then may digitally processed.

The mapping of an input symbol to an output symbol x_(n) depends on thechannel impulse response and the peak power constraint according to theprecoder of FIG. 5.

Step 110 may include step 112, 114 and 116.

Step 112 may include determining whether a transmission of an outputsymbol that equals the input symbol will cause to a deviation from thepeak power constraint at the input of the ADC. In other words—step 112may determine of a certain (for example—the n'th output signal) isforbidden or not.

The determination may be based on various parameters such as the channelstate, the channel impulse response and probability P_(peak). Theseparameters may be known, estimated, or evaluated over time.

The peak power constraint me be (or may be determined based on)probability P_(peak). Denoting P_(n) as the instantaneous power of asignal at an input of an ADC then a peak P_(r) is defined as a value ofP_(n) which exceeded with the probability P_(peak).

PAPR stands for a peak to average power ratio. A PAPR gain (G_(PAPR)) isthe ratio between a PAPR of a system that implements method 100 to aPAPR of a system that does not implement method 100.

RSQNR stands for a receiver signal to quantization noise ratio. TheRSQNR reflects the relationship between the average power of thereceived signal and the quantization noise introduced by the ADC.

A RSQNR gain (G_(PSQNR)) is the reduction in a required power at thereceiver for a given symbol rate—the reduction is measured in relationto a system that does not implement method 100.

The overall shaping gain G_(T) may equal the sum (when represented indB) of G_(PAPR) and G_(PSQNR).

The probability P_(peak) may determine the overall shaping gain G_(T).

If the output signal is not forbidden—then step 112 may be followed bystep 114 of maintaining the input symbol—determining that the outputsymbol may equal the input signal.

If the output signal is forbidden—then step 112 may be followed by step116 of mapping the input symbol to an output symbol that differs fromthe output symbol—to an output symbol that is not forbidden.

Step 116 may include selecting as the output symbol a selected candidatesymbol out of a set of candidates symbols that when transmitted the peakpower constraint at the ADC input is satisfied.

Step 116 may perform the selecting in various manners—for example—byselecting a selected output symbol of the set that has a lowest Hammingdistance from the input symbol, out of the set of candidates symbols.The output symbol should belong to set F. If set F contains manycandidates then, the symbol with the lowest hamming distance is chosen.

Step 116 may include using a channel-state dependent mapping tablecomprising, for each current channel state, quantized values ofprobabilities of a next channel state to become sk, given that thecurrent state is sk-1.

Method 100 may include calculating the set of candidate symbols.

Step 105 may be preceded by performing error correction coding (ECC) toprovide codewords that are then undergo step 110. The ECC may apply aniteratively decodable code that may handle erasures. (here we canexplain that the operation of the precoder is similar to puncturingthough a dynamic one, and each bit punctured is handled by the receiveras an erasure). An example is a turbo code. The codeword may be dividedinto m-tuples b^(m). At time instance n the mapping may include mappingeach b^(m) _(n) into a symbol x_(n).

LLR values computed by the BCJR may be used as a priori input to the ECCencoding.

In each iteration, the decoder produces extrinsic LLR values(Λ^(e))^(mN) which are used as an a priory input to the BCJR module,which in turn calculates new extrinsic LLRs which are sent back to thecode decoder. After a pre-determined number of iterations has beenreached, the bit estimations {circumflex over ( )} u are determined byperforming hard decision on the decoder LLR values (Λ^(e))^(Mn).Initially, all (Λ^(e))^(mN) may be set to zero. The decoding complexitymay be reduced by saturating the BCJR extrinsic LLRs.

Step 110 may be followed by step 120 of transmitting the output symbolby the transmitter.

Steps 110 and 120 may be executed by the transmitter.

The mapping may include imposing a Markovian symbol distribution at anoutput of the transmitter. The Markovian symbol distribution may beoptimal or non-optimal.

For example, the Markovian symbol distribution may be determined to beoptimal for given values of RPQNR and Transmitter Signal to ThermalNoise Ratio (TSTNR).

This may include a first step of finding a maximal entropy Markoviandistributions under peak constraints, and a second step of finding theMarkovian distribution with the highest MI, among the Markoviandistributions calculated in the first step.

The first step may include optimizing the MI with respect to probabilityP_(peak) while keeping TSTNR and PRQNR constant. This step may beimplicit in the online precoder. The online precoder provides anapproximation to the optimal distribution.

Step 120 may be followed by step 130 of receiving, by the receiver, areceived symbol that represents the output symbol. The received symbolmay be altered by the channel.

Step 130 may be followed by step 140 of de-mapping the received symbol,by a de-mapper of the receiver, to a de-mapped symbol that representsthe input symbol.

Step 140 may include reversing the mapping of step 110.

Step 140 may include applying a reduced complexity BJCR process on thereceived symbols, wherein the branches probabilities of each state inthe trellis are calculated on the fly.

FIG. 2 illustrates an example of a turbo encoder 200 that is configuredto implement method 100.

The turbo encoder may include binary turbo encoder 202, multiplexer 204,puncturer 206, bit interleaves 208 and modulator 210.

A binary information stream u is firstly encoded (by binary turboencoder 202) with a rate d/m systematic error correction code (ECC code)into a code word.

The code word is then divided into m-tuples, with m=log₂(M), where ineach tuple the first d bits are information bits (denoted “systematicbits”) and the last m−d bits are parity bits.

Then, at time instance n, the modulator 210 maps (step 110) each m-tuple(of b_(n,0) till b_(n,m−1)) into a symbol from Xn, using a mappingfunction.

According to the channel state at time n, the channel impulse response,and p_(peak), the mapping function calculates a mapping table of size2^(m) by using a bit labeling algorithm. Then, the mapping table is usedto map the m tuple to a symbol Xn.

Due to the astronomical number of states at high symbols rate, themaximal entropy Markovian distribution in may be hard to calculate.

Thus, in the practical scheme described above, the distribution may beactually calculated by the mapping function. The calculated distributionis designed to keep the peak constraint, p_(peak), at the ADC input, butnot to maximize the entropy. Thus, the implementation may be sub-optimaland may result in an insignificant loss compared to optimal solution.

An example of the bit labeling calculation (and thus the symboldistribution), given a channel impulse response, a channel state, andp_(peak), which performs by the mapping function, is describe in thefollowing section. Note, the same mapping function is used in bothtransmitter and receiver.

The goal of the mapping function is to calculate the mapping table atstep n, given channel state, channel impulse response, and p_(peak).This calculation can be divided to two steps. Firstly, the forbiddensymbols at step n (symbols that will result p_(n)>p_(peak)) can easilybe found since that the channel state, the channel impulse response, andp_(peak) are known.

The goal of the bit labeling process is to map all the possible 2^(m)bit combinations at the modulator input, to a constellation symbol. Ifthe set of non-forbidden symbols is empty then the mapping is the Graymapping. Since that not always all the constellation symbols are allowedto be transmitted (set of non-forbidden symbols is not empty), all theGray bit labels of the symbols in the set of non-forbidden symbols areactually free and should be assign to the symbols in the set offorbidden symbols. The assignment is according to the minimum hammingdistance criterion, i.e., each free label should be assigned to a symbolin F, such that there are minimal different bits between the originalGray bit label of the symbol and the free label. The different bitsamong the labels are actually erased and should be decoded right by thereceiver suggested in FIG. 3.

An example of a mapping table of 4-PAM constellation, is presented intable I.

In this example, symbol x=−1 is transmitted with probability 1/2, andsymbols x=1 and x=3 are transmitted with probability 1/4 each. Note thatin this case, symbol x=−3 is transmitted with zero probability and thus,2 labels assigned to symbol x=−1. Therefore, the upper bit is actuallyerased (denoted by X). Note, in the case where all the constellationsymbols can be transmitted, the mapping table is simply the Graylabeling of the constellation.

TABLE I Table I : Symbol Address b0 b1 Point Pr Label 0 0 0 −1 ½ X0 2 10 1 0 1 1 ¼ 01 3 1 1 3 ¼ 11

The receiver 300 includes a maximum a posterior probability (MAP)equalizer 302, de-interleaver 304, demultiplexer 306, binary turbodecoder 308 and puncturer and bit interleaver 310. The MAP equalizerreceives the output of the ADC.

FIG. 5 illustrates an example of a precoder 500. The precoder 500include mapping table 510, buffer 520 and A calculator.

Element b_(n) ^(m) is fed to mapping table 510 of size 2^(Q)×Q (Q is theconstellation size) that outputs x_(n) that is an output signal of theprecoder 500. In addition, x_(n) is fed to a buffer 520 that stores Lprevious values x_(n−1) till x_(n−L+1) that are fed to calculator 530that calculates A.

FIG. 5 also illustrates an example of a mapping table for a 4-PAMconstellations. Other tables may be used for other constellations andeven for the 4-PAM constellation. At the table—col index—index of aninput symbol, row index-decimal representation of A and value-outputsymbol

FIG. 5 also illustrates an example of a calculation of A. Ai has zero ofone value based on whether xi belongs to F or not.

F is calculated by an equation also illustrate din FIG. 5. In thisequation X is a set of all constellation symbols, γ is a peak powerconstraint, and h0 . . . hL−1 are—channel impulse responses.

FIG. 6 illustrates a system 600 that includes a receiver and atransmitter. The transmitter includes error correction encoder (ECC) 602followed by a precoder 604. The precoder 604 is followed by a channel(wired or wireless) that is followed by an ADC (or an analog front endof the receiver followed by the ADC)—in FIG. 600 the channel and ADC arecollectively denoted CH+ADC 606.

The ADC is followed by M-BCJR module 608 and a decoder 610. The decoderoutputs a reconstruction of input signals.

The precoder 604 of FIG. 5 is configured to recover erased bits duringthe BCJR and decoder operation.

FIG. 7 is an example of a process of calculating online the branchprobability in the BCJR Trellis. The calculation involves mapping tableand A calculator.

At the receiver side, shown in FIG. 3, the noisy symbol y_(n) isreceived by MAP equalizer 302. The MAP equalizer may be based on aM-BCJR algorithm, which keeps, at every step, T states with highestmetric. The LLR values Λ^(I)(b_(I)), where 0≤I≤m−1, are produced foreach encoded bit. The LLR values are used, after appropriate bitde-interleaving (by de-interleaver 304), as an a priory input to abinary turbo decoder 308. In each iteration, the binary turbo decoder308 produces extrinsic LLRs which fed via puncturer and bit interleaver310 to MAP equalizer and are used as an a priory input of thecalculation of new extrinsic LLRs which are sent back to the binaryturbo decoder. After a pre-determined number of iterations has beenreached, the bit estimations are determined by performing hard decisionon the turbo decoder's a posterior LLRs.

The extrinsic LLRs Λ¹(b_(I)), for each y_(n), may be calculated usingM-BCJR algorithm applied on the channel states Trellis diagram. For eachy_(n), the BCJR is producing m LLR values. Since the bit labeling ofy_(n) depends on the channel state (i.e., the bit labeling of y_(n) canbe different for each channel state) then, to produce LLR values, thebit label of each survivor state is calculated by using the same mappingfunction used at the transmitter. (see—FIG. 3)

Once the block of noisy symbols y=(y₀, . . . , y_(N−1)) has beenreceived, the M-BCJR algorithm is running, and computesσ_(ijn)=Pr(s_(n−1)=i; s_(n)=j; y)=Pr(s_(n−1)=i; c_(ij); y) for all0≤n≤N−1, and for T states with the highest metrics at step n−1. Thesymbol that results to a transition from state i to state j, denoted byc_(ij).

Next, the BCJR extrinsic LLRs, for each y_(n), can be calculated by

${\Lambda_{n}^{\prime}\left( b_{l} \right)} = {{\log\left( {\sum\limits_{{({i,j})} \in E_{0}}\frac{{\sum_{{c_{i,j}:b_{i}} = 0}\sigma_{{ij}_{n}}} + {\sum_{{c_{ij}:b_{1}} = X}{\sigma_{{ij}_{n}} \cdot P_{0}}}}{{\sum_{{c_{i,j}:b_{i}} = 1}\sigma_{{ij}_{n}}} + {\sum_{{c_{ij}:b_{1}} = X}{\sigma_{{ij}_{n}} \cdot P_{1}}}}} \right)} - {\Lambda_{n}^{e}\left( b_{l} \right)}}$

Where Λ^(e)(b_(I)) is the extrinsic LLR from the Turbo decoder,P₀=Pr(b_(I)=0), and P₁=Pr(b_(I)=1). Initially, all ζ^(e)(b_(I)) are setto 0. The bit probabilities, Pr(b_(I)=0) and Pr(b_(I)=1), are calculatedfrom Λ^(e)(b_(I)). Note, the BCJR module calculates the bit labeling ofeach c_(ij) by the mapping function used at transmitter (FIG. 3)

The decoding complexity can be reduced by manipulating the BCJRextrinsic LLRs, calculated above, according to

${\Lambda_{n}\left( b_{l} \right)} = {\log\left( \frac{\max\left( {{P_{n}\left( {b_{l} = 0} \right)},{K_{n}\left( b_{l} \right)}} \right)}{\max\left( {{P_{n}\left( {b_{l} = 1} \right)},{K_{n}\left( b_{l} \right)}} \right)} \right)}$

For each bit the threshold value Kn(b_(I)) is computer as:

${K_{n}\left( b_{l} \right)} = {\gamma{\max\limits_{b_{l} \in {\lbrack{0,1}\rbrack}}\left( {P_{n}\left( b_{l} \right)} \right)}}$

The bit probabilities P_(n)(b_(I)=0) and P_(n)(b_(I)=1) are calculatedusing the first equation for BCJR extrinsic LLRs, for each y_(n), andthe value of γ is optimized to yield the best BER performance.

FIG. 4 illustrates method 400 for Peak to Average Power Ratio (PAPR)reduction at an input of analog to digital converter (ADC) of thereceiver.

Method 400 may start by step 410 of mapping, by a mapper, an inputsymbol to an output symbol that maintains a peak power constraint at theinput of the ADC; wherein the mapping is responsive to previouslytransmitted symbols.

Step 410 may include selecting (412) as the output symbol a selectedcandidate symbol out of a set of candidates symbols that whentransmitted the peak power constraint at the ADC input is satisfied,when determining whether a transmission of an output symbol that equalsthe input symbol will cause to a deviation from the peak powerconstraint at the input of the ADC.

Step 410 may be the same as step 110 or may differ from step 110.

According to an embodiment of the disclosure there may be provided astep of mapping, by a mapper, of an input symbol (referred to as acurrent input symbol) to an output symbol (referred to as a currentoutput symbol) that maintains a peak power constraint at the input ofthe ADC. The mapping is responsive to (a) previously transmittedsymbols, and also to (b) state of the channel following a transmissionof the current output symbol.

The state of the channel changes after the transmission of each outputsymbol—and the mapping may take into account next output symbols to betransmitted after the current output symbol.

For example—the mapping may check whether the state of the channel willallow to transmit the one or more next symbols—and may prevent atransmission of a current output symbol that prevent a transmission ofany output symbol during one or more points of time that follow thetransmission of the current output symbol.

The one or more next output symbols may be within a time window thatfollows the transmission of the current output symbol. The time windowmay be limited to include only the next output symbol. The time windowmay or may not exceed the delay of the channel. The delay D of thechannel is the gap between the first tap of the channel impulse responseand the tap of maximal intensity of the channel impulse response. Inother words—the delay is the number of taps that takes to the channelimpulse response, h^(L), to reach its maximal value.

This embodiment may be included in method 100. For example—executingstep 110 for mapping, by a mapper, an input symbol to an output symbolthat maintains a peak power constraint at the input of the ADC of thereceiver—whereas the mapping is responsive to (a) previously transmittedsymbols, and also to (b) next symbols to be transmitted after thecurrent output symbol.

FIG. 8 illustrates method 401 that include step 411 and step 412.

Step 411 replaces step 410 of FIG. 400 and includes mapping, by amapper, an input symbol to an output symbol that maintains a peak powerconstraint at the input of the ADC of the receiver. The mapping isresponsive to previously transmitted symbols and to candidates for nexttransmitted symbols. Especially—the mapping is responsive to the currentstate of the channel (based at least in part on the previouslytransmitted symbols)—and to the state of the channel within a timewindow that follows the transmission of the current output symbol.

Accordingly—in order to ensure that at least one output symbol isallowed for transmission in every time step the mapping may be asfollows.

In every time step n, the precoder maps m=log 2(M) coded bits to anoutput symbol x_(n) that satisfies first peak power constraint p_(n)≤γ.To do so, the precoder firstly calculates the allowed symbols fortransmission at step n according to the channel state s^(L−1), wheres^(L−1) is defined by the last L−1 transmitted symbols.

A second constraint is added and refers to the state of the channelafter the transmission of the current output symbol—within a timewindow.

The second constraint should prevent a situation in which a transmissionof an output symbol that satisfies p_(n)≤γ would cause that none of theconstellation symbols are allowed for transmission in the next timewindow. The time window may or may not exceed D.

In order to ensure that in the next D channel states (or within a timewindow that exceed D or may equal D) at least one allowed symbol exists,an allowed output symbol in the current time step n should fulfill thefollowing conditions: (a) it does not cause peak deviation in thecurrent time step (i.e., p_(n)≤γ) and (b) at least one symbol is allowedfor transmission (i.e., does not cause peak deviation) in the next Dchannel states.

Thus—if during the time window there is at least one time in which nooutput symbol can be transmitted (due to the state of the channel atthat time)—there is a need to find another output symbol that will allowthe transmission of one all combinations of output symbols can betransmitted at that time.

Example of the Algorithm for D=1 is shown below. Higher D values requireto evaluate combinations of multiple output symbols during multipletimes.

Input: channel state s^(L−1), channel impulse response h^(L), peakconstraint γ, constellation X Output: A^(M) (M is constellationcardinality) Init: A[1 X M] = (false, false, ... , false) Algorithm forD = 1 : For i = 1: M do p = |X[i] · h[1] + Σ_(k=2) ^(L)s[k − 1] · h[k]|² If p ≤ γ then s[1] ← X[i] s[2: L − 1] ← s[1: L − 2]  else  continue End if  For j = 1: M do p = |X[j] · h[1] + Σ_(k=2) ^(L)s[k − 1] ·h[k]|²  If p ≤ γ then A[i] ←true  break  End if   End for End for

In the foregoing specification, the invention has been described withreference to specific examples of embodiments of the invention. It will,however, be evident that various modifications and changes may be madetherein without departing from the broader spirit and scope of theinvention as set forth in the appended claims.

Moreover, the terms “front,” “back,” “top,” “bottom,” “over,” “under”and the like in the description and in the claims, if any, are used fordescriptive purposes and not necessarily for describing permanentrelative positions. It is understood that the terms so used areinterchangeable under appropriate circumstances such that theembodiments of the invention described herein are, for example, capableof operation in other orientations than those illustrated or otherwisedescribed herein.

Those skilled in the art will recognize that the boundaries betweenlogic blocks are merely illustrative and that alternative embodimentsmay merge logic blocks or circuit elements or impose an alternatedecomposition of functionality upon various logic blocks or circuitelements. Thus, it is to be understood that the architectures depictedherein are merely exemplary, and that in fact many other architecturescan be implemented which achieve the same functionality.

Any arrangement of components to achieve the same functionality iseffectively “associated” such that the desired functionality isachieved. Hence, any two components herein combined to achieve aparticular functionality can be seen as “associated with” each othersuch that the desired functionality is achieved, irrespective ofarchitectures or intermedial components. Likewise, any two components soassociated can also be viewed as being “operably connected,” or“operably coupled,” to each other to achieve the desired functionality.

Furthermore, those skilled in the art will recognize that boundariesbetween the above described operations merely illustrative. The multipleoperations may be combined into a single operation, a single operationmay be distributed in additional operations and operations may beexecuted at least partially overlapping in time. Moreover, alternativeembodiments may include multiple instances of a particular operation,and the order of operations may be altered in various other embodiments.

However, other modifications, variations and alternatives are alsopossible. The specifications and drawings are, accordingly, to beregarded in an illustrative rather than in a restrictive sense.

In the claims, any reference signs placed between parentheses shall notbe construed as limiting the claim. The word ‘comprising’ does notexclude the presence of other elements or steps then those listed in aclaim. Furthermore, the terms “a” or “an,” as used herein, are definedas one as or more than one. Also, the use of introductory phrases suchas “at least one” and “one or more” in the claims should not beconstrued to imply that the introduction of another claim element by theindefinite articles “a” or “an” limits any particular claim containingsuch introduced claim element to inventions containing only one suchelement, even when the same claim includes the introductory phrases “oneor more” or “at least one” and indefinite articles such as “a” or “an.”The same holds true for the use of definite articles. Unless statedotherwise, terms such as “first” and “second” are used to arbitrarilydistinguish between the elements such terms describe. Thus, these termsare not necessarily intended to indicate temporal or otherprioritization of such elements the mere fact that certain measures arerecited in mutually different claims does not indicate that acombination of these measures cannot be used to advantage.

While certain features of the invention have been illustrated anddescribed herein, many modifications, substitutions, changes, andequivalents will now occur to those of ordinary skill in the art. It is,therefore, to be understood that the appended claims are intended tocover all such modifications and changes as fall within the true spiritof the invention.

Any combination of any component of any device that is illustrated inany of the figures and/or specification and/or the claims may beprovided.

Any combination of steps, operations and/or methods illustrated in anyof the figures and/or specification and/or the claims may be provided.

Any combination of operations illustrated in any of the figures and/orspecification and/or the claims may be provided.

Any combination of methods illustrated in any of the figures and/orspecification and/or the claims may be provided.

The invention claimed is:
 1. A method for communication by symbols, themethod comprising: mapping, by a mapper, an input symbol to an outputsymbol such that reception of the output symbol by a receiver maintainsa peak power constraint at an input of the receiver; wherein the mappingis responsive to a state of a communication channel to said receiverfollowing a transmission of said output symbol; transmitting the outputsymbol by a transmitter over the communication channel; thereby enablingto reduce a Peak to Average Power Ratio (PAPR) at the input of thereceiver.
 2. The method according to claim 1, wherein said output symbolhaving a certain value, and wherein the mapping comprises determiningwhether transmission of said output symbol having said certain valuewill affect a deviation from the peak power constraint at the input ofthe receiver upon transmission of an additional output symbol of anyvalue over the communication channel during a time window that followssaid transmitting of the output symbol.
 3. The method according to claim2, wherein the mapping comprises setting said output symbol with a valuethat differs from said certain value upon determining that said state ofthe communication channel following said transmitting of the outputsymbol of the certain value will affect said deviation upon thetransmission of the additional output symbol of any value over thecommunication channel during said time window.
 4. The method accordingto claim 1, wherein the mapping is further responsive to previouslytransmitted symbols.
 5. The method according to claim 1, operableaccording to at least one of the following: i. the mapping comprisesimposing a Markovian symbol distribution at an output of thetransmitter; ii. the mapping is set regardless of a maximization ofentropy; iii. the mapping comprises calculating a set of one or morecandidate symbols that when transmitted instead of said input symbol,maintain said peak power constraint at the input of the receiver; iv.the mapping is responsive to an impulse response of the communicationchannel and to the peak power constraint at the input of the receiver;v. wherein said input of the receiver being an input of analog todigital converter (ADC) of the receiver.
 6. The method according toclaim 1, wherein the mapping comprises: determining whether saidtransmission of the output symbol with a value that equals the inputsymbol will affect a deviation from the peak power constraint at theinput of the receiver; and upon determining that said deviation will beaffected by said transmission selecting said output symbol from a set ofcandidate symbols that maintain said peak power constraint at an inputof an ADC of the receiver.
 7. The method according to claim 6, whereinsaid selecting is such that, the output symbol being selected from theset of candidate symbols has a lowest Hamming distance from the inputsymbol.
 8. The method according to claim 1, further comprisingreceiving, by the receiver, a received symbol that represents the outputsymbol; and de-mapping the received symbol, by a de-mapper of thereceiver, to a de-mapped symbol that represents the input symbol.
 9. Themethod according to claim 8, wherein the de-mapping comprises applyingmaximum a posteriori decoding process on the received symbol, whereinthe branches probabilities of each state in a trellis are calculated onthe fly.
 10. The method according to claim 1, wherein the mappingcomprises using a channel-state dependent mapping table comprising, foreach channel state sk-1, quantized values of probabilities of thechannel state to become a next channel state sk, given that the channelstate is sk-1.
 11. A method for Peak to Average Power Ratio (PAPR)reduction at an input of analog to digital converter (ADC) of areceiver, the method comprising: mapping, by a mapper, an input symbolto an output symbol that maintains a peak power constraint at the inputof the ADC of the receiver; wherein the mapping is responsive to a stateof a communication channel to said receiver following a transmission ofa current output symbol; wherein upon determination that a transmissionof the output symbol that equals the input symbol will cause to adeviation from the peak power constraint at the input of the ADC of thereceiver, the mapping comprises selecting as the output symbol aselected candidate symbol out of a set of candidate symbols that whentransmitted the peak power constraint at the input of the ADC of thereceiver is satisfied.
 12. A system, comprising: a transmitter thatcomprises: (i) a mapper that is configured to map an input symbol to anoutput symbol that maintains a peak power constraint at an input of ananalog to digital converter (ADC) of a receiver; wherein the mapping isresponsive to a state of a communication channel to said receiverfollowing a transmission of a current output symbol; and (ii) atransmission circuit that is configured to transmit the output symbol.13. The system of claim 12, comprising the receiver, wherein thereceiver comprises: (i) an interface that is configured to receive areceived symbol that represents the output symbol; and (ii) a de-mapperthat is configured to de-map the received symbol, to a de-mapped symbolthat represents the input symbol.
 14. The system of claim 12, whereinthe mapper is configured to carry out at least one of the following:determining said state of the communication channel following saidtransmission whereby said determining of said state comprises checkingwhether transmission of the output symbol of a certain value will affecta deviation from the peak power constraint at the input of the ADC ofthe receiver upon transmission of an additional output symbol of anyvalue over the communication channel during a certain time window thatfollows the transmission of the output symbol; and setting said outputsymbol with a value that differs from said certain value upondetermining that said state of the communication channel following saidtransmission of the output symbol of the certain value, will affect thedeviation from the peak power constraint at the input of the ADC of thereceiver upon transmission of the additional output symbol of any valueover the communication channel during the certain time window thatfollows the transmission.
 15. The system according to claim 12, whereinthe mapping is further responsive to previously transmitted symbols. 16.At least one non-transitory computer readable medium that storesinstructions for Peak to Average Power Ratio (PAPR) reduction at aninput of an analog to digital converter (ADC) of a receiver of a system,wherein the instructions, once executed by the system, cause the systemto carry out mapping, by a mapper of a transmitter of the system, of aninput symbol to an output symbol that maintains a peak power constraintat the input of the ADC of the receiver; wherein the mapping isresponsive to a state of a communication channel to said receiverfollowing a transmission of a current output symbol; and transmittingthe output symbol by the transmitter.
 17. The at least onenon-transitory computer readable medium according to claim 16, whereinone or more of the following: said mapping comprises imposing aMarkovian symbol distribution at an output of the transmitter saidmapping is set regardless of a maximization of entropy; said mappingcomprises calculating a set of one or more candidate symbols that whentransmitted instead of said input symbol, maintain said peak powerconstraint at the input of the ADC of the receiver; said mapping isresponsive to a channel impulse response and to the peak powerconstraint at the input of the ADC of the receiver; and said mappingcomprises using a channel-state dependent mapping table comprising, foreach current channel state, quantized values of probabilities of a nextchannel state to become sk, given that a current state is sk-1.
 18. Theat least one non-transitory computer readable medium according to claim16, wherein the mapping comprises: determining whether the transmissionof the output symbol that equals the input symbol will cause to adeviation from the peak power constraint at the input of the ADC of thereceiver; and when determining that the deviation from the peakconstraint, then selecting as the output symbol a selected candidatesymbol out of a set of candidate symbols that when transmitted the peakpower constraint at the input of the ADC of the receiver is satisfied.19. The at least one non-transitory computer readable medium accordingto claim 18 that stores instructions for selecting the selected outputsymbol of the set, the selected output symbol of the set has a lowestHamming distance from the input symbol, out of the set of candidatesymbols.
 20. The at least one non-transitory computer readable mediumaccording to claim 16, wherein the mapping comprises at least one of thefollowing: determining said state of the communication channel followingsaid transmission whereby said determining of said state compriseschecking whether transmission of the output symbol of a certain valuewill affect a deviation from the peak power constraint at the input ofthe ADC of the receiver upon transmission of an additional output symbolof any value over the communication channel during a certain time windowthat follows the transmission of the output symbol; and setting saidoutput symbol with a value that differs from said certain value upondetermining that said state of the communication channel following saidtransmission of the output symbol of the certain value, will affect thedeviation from the peak power constraint at the input of the ADC of thereceiver upon the transmission of the additional output symbol of anyvalue over the communication channel during the certain time window thatfollows the transmission.
 21. The at least one non-transitory computerreadable medium according to claim 16, wherein the instructions, onceexecuted by the system, further cause the system to carry out:receiving, by the receiver, a received symbol that represents the outputsymbol; and de-mapping the received symbol, by a de-mapper of thereceiver, to a de-mapped symbol that represents the input symbol. 22.The at least one non-transitory computer readable medium according toclaim 21, wherein the de-mapping comprises applying a maximum aposteriori decoding process on the received symbol, wherein the branchesprobabilities of each state in a trellis are calculated on the fly.